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Observer design estimating the propofol concentration in PKPD model with feedback control of anesthesia administration

Ilyas Muhammad, Khan Awais, Khan Muhammad Abbas, Xie Wei, Riaz Raja Ali, Khan Yousaf

Archives of Control Sciences

2022

Vol. 32, No. 1

85--103

Propofol infusion in anesthesia administration requires continual adjustment in the manual infusion system to regulate the hypnosis level. Hypnotic level is based on Bispectral Index Monitor (BIS) showing the cortical activity of the brain scaled between 0 to 100. The new challenging aspect of automation in anaesthesia is to estimate the concentration of hypnotic drugs in different compartments of the body including primary, rapid peripheral (muscle), slow peripheral (bones, fat) and effect site (brain) compartment based on Pharmacokinetics (PK) and Pharmacodynamics (PD) model. This paper aimed to regulate the hypnosis level with estimating the Propofol concentrations using a linear observer in feedback control strategy based on Integral Super-Twisting Sliding Mode Controller (ISTSMC). The drug concentration in plasma of the silico patients accurately estimated in nominal transient. The results show that tracking errors between the actual output in form of BIS level and linearized output nearly approaches to zero in the maintenance phase of anesthesia to ensure the controller response on sliding phase with optimum performances by achieving desired hypnotic level 50 on BIS. The robustness of control strategy is further ensured by adding measurement noise of electromagnetic environment of operation theatre distracting signal quality index of the output BIS level.

Sufficient conditions for optimality for a mathematical model of drug treatment with pharmacodynamics

Leszczynski M., Ratajczyk E., Ledzewicz U., Schättler H.

Opuscula Mathematica

2017

Vol. 37, no. 3

403--419

We consider an optimal control problem for a general mathematical model of drug treatment with a single agent. The control represents the concentration of the agent and its effect (pharmacodynamics) is modelled by a Hill function (i.e., Michaelis-Menten type kinetics). The aim is to minimize a cost functional consisting of a weighted average related to the state of the system (both at the end and during a fixed therapy horizon) and to the total amount of drugs given. The latter is an indirect measure for the side effects of treatment. It is shown that optimal controls are continuous functions of time that change between full or no dose segments with connecting pieces that take values in the interior of the control set. Sufficient conditions for the strong local optimality of an extremal controlled trajectory in terms of the existence of a solution to a piecewise defined Riccati differential equation are given.